Mr. Fidler, an attorney by trade, could serve as counsel or as an adviser, though his role still needs to be defined and talks remain fluid.

The move represents the first of the expected spoils for the Brooklyn Democratic Party, which was a key partner in the deal brokered by labor unions and Mayor Bill de Blasio to elect Ms. Mark-Viverito speaker yesterday.

“As part of the deal with Brooklyn, Lew Fidler is slated to have an advisory level position with Speaker Mark-Viverito,” said one council source. “It’s what Brooklyn wanted.”

For his part, Mr. Fidler told Politicker he hoped to serve in the new council but that no role had been guaranteed.

“I do hope to play a role at least on a part-time basis in ensuring that the new council succeeds,” Mr. Fidler said in an email. “But nothing is done nor firm, and no titles or roles have been promised or given.”

Unlike Ms. Mark-Viverito, who was a staunch de Blasio ally during the Democratic primary, Mr. Fidler was a staunch critic who endorsed the candidate backed by Brooklyn’s Democratic Party: Bill Thompson. Mr. de Blasio and Mr. Fidler, both former Brooklyn councilman, had been at odds since Mr. de Blasio moved to oust Mr. Fidler as leader of the council’s Brooklyn delegation a decade ago.

Ms. Mark-Viverito declined to comment on Mr. Fidler’s role but said last night on NY1 she hopes to make appointments soon.